Agreed, do it from the inside, that's the way the manufacture’s continue to engineer it. Rust protection on the outside, heat and sound insulation on the inside. You can order a replacement firewall pad if yours is missing or disintegrated.

Also, there are products like Dynomat that are made for reduincg sound and heat. I hear McMaster-Car has the same material, but for about 20% of the price of Dynomat.

Roofing material can work for the floor, but is considered the least affective in heat and sound control. Basically, it can melt and produce a smell if the temp is too high.